Here is a schematic of what I guess you are asking about. The value of the resistors depends on the voltage you use and the current requirements of the LED's. Post those and someone will tell you the value of the resistors required.

If you are planning on using a 9v PP3 "transistor" battery, be aware that just 1 LED drawing 20mA current is a pretty heavy load for it; the battery will be drained in 1 day.

You will be better off to use a plug-type regulated supply, or AA rechargeable batteries; 4 in series to get 4.8v.

You need to calculate your current limiting resistors as:
Rlimit >= (Vsupply - Vf_LED) / Desired_Current
where:
Rlimit - is the value of resistance in Ohms that you will need to limit the LED current to a safe level.

Vsupply - is the voltage that you will be placing across the LED and its' current limiting resistor.

Vf_LED - The typical Vf @ current that is specified in the LED's data sheet or packaging. Vf means "Forward Voltage"; it is the voltage drop across the LED itself when a certain amount of current is flowing through it in the forward biased direction. If you don't have that information, then help us suggest values by telling us about your LEDs; where you bought them, a link to the site, part number, etc.

Desired_Current - this is the current that was specified with the typical Vf information; you can use less, but should not use more or you will damage your LEDs.

Let's say you are using four rechargeable AA batteries in series that have a total of 4.8v output, and that you have red LEDs with a typical Vf of 2v @ 20mA.
You calculate:
Rlimit >= (4.8v - 2v) / 20mA = 2.8v / 0.02 = 140 Ohms.

There is a decade table of standard resistance values here:http://www.logwell.com/tech/components/resistor_values.html (Bookmark this page!)
Looking at the E12 (yellow) and E24 (green) columns, the closest standard value >= 140 Ohms is 150 Ohms; so the current will be reduced a little from 20mA but it will be hard to tell the difference. We can work the formula backwards to see what the current will be:
Iled = (4.8v - 2v) / 150 Ohms = 2.8/150 = 18.7mA; that's 93.5% of 20mA.

I wish to use red LEDs. Initially I wanted to use 9V, on the other hand is the 4.8v output suggested by sgtwookie lasting?

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Much longer than the 9V, yes. If you want to use the 9V, it might work if you only have 1 or 2 LEDs on at any one time and none of them on most of the time. But if you want more than a couple on for extended times, the 9V is a poor choice.

To accomplish what you described, and to build the circuit in the schematic, yes. Don't buy resistors until you make sure of the current to be used for each LED and the voltage of your supply. Sarge has shown you the calculations to follow. You'll want to shop for switches, as those will be the costliest part of your project.

sorry , this is the image. I have yet to put in the switches in the image. The image by tracecom will best represent my project...

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Gee, then why did you post this image when Tracecom's image is more like how you need to build it?

I wish to use red LEDs.

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Small red LEDs may have Vf's somewhere between 1.7v and 2.3v or so - it depends on the manufacturer's rating. You also need to specify the current.

Initially I wanted to use 9V

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If you want to start off using 9v, then you will need resistors that are much higher in value.
Rlimit >= (Vsupply - Vf_LED) / Desired_current ... remember?

, on the other hand is the 4.8v output suggested by sgtwookie lasting?

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They will last a lot longer than a 9v pp3 "transistor" battery.

I have to purchase 10 x 140 Ohms resistor, 10 LED, and 10 switches?

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I guess you didn't read what I wrote. 140 Ohms is not a standard value of resistance. 150 Ohms was the closest standard value for the example I gave. If you used 140 Ohms or 150 Ohms with an led that had a Vf of 2v and a 9v battery, then you would have far too much current flowing through your LEDs. For example, (9v-2v)/140 = 50mA; 2.5 times what the example LEDs were rated for.

Will all the LED share the same degree of brightness?

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Some may be brighter, some may be dimmer. In any given batch of LEDs, 75% to 85% will have very close to the same Vf, but the remainder may be as much as ±10% different from the average.

And are there any possible usage of IC to do this? I have seen on youtube, he is able to control 6 switches to 6 led respectively. But that's tough for me...